{
  "id": "1208.2184",
  "version": "v2",
  "published": "2012-08-10T14:18:02.000Z",
  "updated": "2014-07-09T23:41:59.000Z",
  "title": "The realizability of operations on homotopy groups concentrated in two degrees",
  "authors": [
    "Hans-Joachim Baues",
    "Martin Frankland"
  ],
  "comment": "Version 2: Some minor corrections. A few changes to the exposition. To appear in the Journal of Homotopy and Related Structures",
  "doi": "10.1007/s40062-014-0086-3",
  "categories": [
    "math.AT"
  ],
  "abstract": "The homotopy groups of a space are endowed with homotopy operations which define the \\Pi-algebra of the space. An Eilenberg-MacLane space is the realization of a \\Pi-algebra concentrated in one degree. In this paper, we provide necessary and sufficient conditions for the realizability of a \\Pi-algebra concentrated in two degrees. We then specialize to the stable case, and list infinite families of such \\Pi-algebras that are not realizable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-09T23:41:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q35",
      "55Q40",
      "55Q45",
      "55Q15",
      "55P20"
    ],
    "keywords": [
      "homotopy groups",
      "realizability",
      "list infinite families",
      "sufficient conditions",
      "eilenberg-maclane space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2184B"
    }
  }
}